Sampled-Output-Data-Driven-Based Adaptive Observer Design and Offline Fault Estimation for T–S Fuzzy Descriptor Systems

In this article, the offline fault estimation via a sampled-output-data-driven adaptive observer is investigated for a class of Takagi–Sugeno fuzzy descriptor nonlinear systems. The additive actuator faults and disturbances are involved. At the signal receiving end, the discrete sampled output signals from systems are obtained through wireless transmission. To achieve the offline fault estimation for the fuzzy descriptor system, the cubic spline interpolation fitting approach is first applied to fit the receiving sampled output data into a dynamic fitting function. Then, the dynamic fitting function is further applied to construct and drive an adaptive observer related to the system in consideration. Compared with the existing observers, the designed discrete sampled-output-data-driven adaptive observer does not require interface docking with the original system equipment. The fault on the system can be estimated offline with a certain degree of accuracy via the provided observer. Stability conditions for the estimation error dynamics are given, which can be converted into linear matrix inequalities. Finally, two numerical models are used to validate the effectiveness of the proposed offline fault estimation method.